Elastic-plastic buckling of externally pressurized auxetic domes

• Negative Poisson’s Ratio (NPR), can significantly increase buckling strength. • Sandwich and two-layer auxetic domes are assessed for buckling behaviour. • Optimally designed dome illustrates the scope the NPR can provide. The paper studies the effect of inclusion of auxetic layer(s), into the wall of externally pressurized torispherical shells, on buckling. Both the base and auxetic layers are assumed to be isotropic and undergo elastic-plastic behavior. In the first instance, load carrying capacities are computed for the Negative Poisson’s Ratio (NPR), within -0.9 and +0.3, and for various wall configurations including: (i) single auxetic layer, (ii) sandwich wall with the auxetic layer embedded between two metallic faces, and (iii) two layer wall with the metallic outer layer and auxetic inner layer. Substantial gains in magnitudes of buckling pressure are recorded depending on the wall construction. This heavily depends on the diameter-to-wall thickness (D/t)-ratio varying between 500 and 2000. Next, the influence of Young’s modulus of the auxetic layer on buckling strength was examined. For E auxetic equal to 10 % of E steel , in two layer head (0.25t-steel and 0.75t-auxetic), one is able to have the same load carrying capacity as if the head had 100 % metallic wall. Finally, structural optimization was employed to assess buckling strength on a like-for-like basis due to large variability in magnitude of buckling pressure. In one specific case, the ratio of the best to the worst buckling pressure, within the admissible design parameters, was found to be 4.8. Large gains in the magnitudes of buckling pressure were also recorded for other optimal configurations. Zero order search technique coupled with a reliable re-analysis tool was employed here.